This is an announcement for the paper "A hyperplane inequality for measures of unconditional convex bodies" by Alexander Koldobsky. Abstract: We prove an inequality that extends to arbitrary measures the hyperplane inequality for volume of unconditional convex bodies originally observed by Bourgain. Archive classification: math.MG math.FA Mathematics Subject Classification: 52A20 Submitted from: koldobskiya@missouri.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1312.7048 or http://arXiv.org/abs/1312.7048